# Charging the Conformal Window

### Abstract

We investigate the properties of near-conformal dynamics in a sector of large charge when approaching the lower boundary of the conformal window from the chirally broken phase. To elucidate our approach we use the time-honored example of the phenomenologically relevant SU(2) color theory featuring $N_f$ Dirac fermions transforming in the fundamental representation of the gauge group. In the chirally broken phase we employ the effective pion Lagrangian featuring also a pseudo-dilaton to capture a possible smooth conformal-to-non-conformal phase transition. We charge the baryon symmetry of the Lagrangian and study its impact on the ground state and spectrum of the theory as well as the would-be conformal dimensions of the lowest large-charge operator. We moreover study the effects of and dependence on the fermion mass term.

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